A089922 -id:A089922 - cp's OEIS frontend

A038395 Concatenation of the first n odd numbers in reverse order.

1, 31, 531, 7531, 97531, 1197531, 131197531, 15131197531, 1715131197531, 191715131197531, 21191715131197531, 2321191715131197531, 252321191715131197531, 27252321191715131197531, 2927252321191715131197531, 312927252321191715131197531

Offset: 1

M. I. Petrescu (mipetrescu(AT)yahoo.com)

a(n) starts with the digits of 2n-1. Indices of prime or probable prime terms are 1,2,37,62,409,...: see also A089922. - M. F. Hasler, Apr 13 2008

If n == 0 (mod 3), so is a(n). - Sergey Pavlov, Mar 29 2017

Mihaly Bencze [Beneze] and L. Tutescu, Some Notions and Questions in Number Theory, Sequence 3.

Florentin Smarandache, Sequences of Numbers Involved in Unsolved Problems, arXiv:math/0604019 [math.GM], 2006.

Cf. A089922, A109837, A038394-A038399, A019518, A019519.

Table[FromDigits[Flatten[IntegerDigits/@Join[Reverse[Range[1,n,2]]]]], {n,1,29,2}] (* Harvey P. Dale, Jun 02 2011 *)

t=""; for( n=1,10^3, ( t=eval( Str( 2*n-1,t))) & print(n" "t)) \\ M. F. Hasler, Apr 13 2008

def a(n): return int("".join(map(str, range(2*n-1, 0, -2))))
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Jan 31 2021

Edited and extended by M. F. Hasler, Apr 13 2008

Edited by T. D. Noe, Oct 30 2008

A109837 Smallest prime factor of the reverse concatenation of the first n odd numbers.

Original entry on oeis.org

31, 3, 17, 7, 3, 1579, 17, 3, 2677, 131, 3, 54049423, 47, 3, 487, 25541, 3, 7, 211, 3, 31, 622639, 3, 498508631, 7, 3, 1259, 193, 3, 7669, 16229, 3, 13, 887377, 3, 737169676563615957555351494745434139373533312927252321191715131197531

Offset: 2

Zak Seidov, Jul 04 2005

Sequence starts with offset 2 since A038395(1)=1 has no prime factor. - M. F. Hasler
Starting with 2nd term each 3rd term is a(3m)=3.
Sequence A089922={3,73,123,817,...} lists the largest odd number (2n-1) used in the terms a(n) which are primes or probable primes.

			n=6: a(6)=1579 because 131197531=1579*83089.

Sean A. Irvine, Table of n, a(n) for n = 2..103

Cf. A038395, A089922, A104644, A138965.

s=1;Do[news=FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[s]}]];fi=FactorInteger[news][[1, 1]];Print[fi];s=news, {n, 3, 70, 2}]

t=1; for( n=2,99, print1( factor( eval( t=Str( 2*n-1,t)))[1,1],", ")) \\ M. F. Hasler, Apr 13 2008

a(n) = A020639(A038395(n)). - R. J. Mathar, Sep 16 2007

More terms from R. J. Mathar, Sep 16 2007
Edited by M. F. Hasler, Apr 14 2008
Edited by T. D. Noe, Oct 30 2008

A261716 Odd numbers that result in a prime when their cubes are concatenated with the cubes of all smaller odd numbers in descending order.

Original entry on oeis.org

3, 27, 115, 643

Offset: 1

Felix Fröhlich, Aug 29 2015

			A000578(3) = 27. The only odd number less than 3 is 1 with A000578(1) = 1. Concatenating the two resulting cubes in descending order one gets 271 which is prime, so 3 is a term of the sequence.

G. L. Honaker, Jr. and C. Caldwell, 19683...25271 (51-digits)

Cf. A091314, A089922.

fQ[n_] := PrimeQ[ FromDigits[ Flatten[ IntegerDigits[ Range[2n - 1, 1, -2]^3]]]]; k = 1; lst = {}; While[k < 1501, If[ fQ[k], AppendTo[lst, 2k - 1]; Print[2k - 1]]; k++]; lst (* Robert G. Wilson v, Sep 16 2015 *)

odd(n) = 2*n-1
con(n) = s=""; k=n; while(k > 0, s=Str(s, Str(odd(k)^3)); k--); eval(s)
isok(n) = ispseudoprime(con(n))
terms(n) = i=0; x=1; while(i < n, if(isok(x), print1(odd(x), ", "); i++); x++)
terms(4) \\ print initial four terms

First 4 terms confirmed by Robert G. Wilson v, Sep 16 2015 and no more < 3000.

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A038395 Concatenation of the first n odd numbers in reverse order.

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A109837 Smallest prime factor of the reverse concatenation of the first n odd numbers.

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A261716 Odd numbers that result in a prime when their cubes are concatenated with the cubes of all smaller odd numbers in descending order.

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Mathematica

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